WIAS Preprint No. 613, (2000)

A model of a general elastic curved rod


Authors

  • Ignat, Anca
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604
  • Tiba, Dan

2010 Mathematics Subject Classification

  • 65N30 34B60 74B99

Keywords

  • Deformation of elastic rods, low geometrical regularity, variable cross sections

DOI

10.20347/WIAS.PREPRINT.613

Abstract

We indicate a new approach to the deformation of three-dimensional curved rods with variable cross section. The model consists of a system of nine ordinary differential equations for which we prove existence and uniqueness via the coercivity of the associated bilinear form. From the geometrical point of view, we are using the Darboux frame or a new local frame requiring just a once continuously differentiable parametrization of the curve. Our model also describes the deformation occurring in the cross sections of the rod.

Appeared in

  • Math. Methods App. Sci. 25 (2002), no. 10, pp. 835-854

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